Download Quadratic Inequalities :  Example 1  (4) Quadratic Inequalities.notebook

(4) Quadratic Inequalities.notebook
Quadratic Inequalities
Example 1 (one variable inequality): How? The trick to solving a quadratic inequality is to replace the inequality symbol with an equal sign and solve the resulting equation. The solutions to the equation will allow you to establish intervals that will let you solve the inequality.
1.
Great "OR" Shade outside
Change the inequality to = and solve:
{x < ­3 or x > 4}
INEQUALITY SHORT CUT: If the original inequality was : “greater than” ­ shade the outside of the number line.
“less than” ­ shade in between the numbers
1. Make sure zero is on one side of the inequality.
2. Factor the quadratic.
3. Plot the zeros on the number line. < > open circles
≤ ≥ closed circles
4. > 0 or ≥ 0 great"or"
solution is away from the zeros
< 0 or ≤ 0 less th"and" solution is between the zeros
(4) Quadratic Inequalities.notebook
2.
Using a number line, graph the solution set of
Great"OR" : away
(x + 1)(x ­ 5) = 0
x = ­1 x = 5
ANSWER: x < ­1 or x > 5
3.
Graph and state the solution set of Less Th"AND" between
(x + 5)(x ­ 5) = 0
x = ­5 x = 5
ANSWER: ­5 < x < 5 4. Solve algebraically:
(x + 1)(x + 7) = 0
x = ­1 x = ­8
­7
­1
x < ­7 or x > ­1
5. 2x2 + 4x > x2 ­ x ­ 6
x2 + 5x + 6 ≥ 0
(x + 2)(x + 3) = 0
x = ­2 x = ­3
­3
­2
x ≤ -3 or x ≥ -2
(4) Quadratic Inequalities.notebook
6. 5x2 + 2x < 0
x(5x + 2) = 0
x = 0 x = ­2/5
­2/5
GCF!!!
0
­2 < x < 0
5
7. 3x2 + 10x < 8
3x2 + 10x ­ 8 < 0
3x2 + 12x ­ 2x ­ 8 = 0
3x(x + 4) ­ 2(x + 4) = 0
(3x ­ 2)(x + 4) = 0
x = 2/3 x = ­4
­4
­4 < x < 2
3
2/3
Case II !!!!